Timo Reuter^1,, Wolfgang Schnotz², Renate Rasch³

External representations play a central role in the process of word problem solving. This study aimed to shed light on teacher-provided representations as cognitive tools for primary students when working on non-routine word problems. Non-routine word problems are characterized by the fact that they cannot be solved by simply applying familiar routine calculations due to their demanding mathematical structure or complex situations described in the problem text. Since primary students often do not generate external representations, the present study examined the questions if providing students with a representation facilitates problem solving in general, and, more in detail, what type of representation (table or drawing) and what level of pre-structuring provided in the representation is most helpful. In an experimental design we studied a sample of 199 4th-graders who worked on non-routine word problems. The experimental design consisted of three tests: A pre-, a treatment-, and a transfer-test. In the pre-test, we measured participant’s prior performance with non-routine word problems. In the treatment-test, an experimental group received problems accompanied by tables and drawings with different levels of pre-structuring to measure student’s performance when external representations were provided for the problem solving process. A control group received no representations. In the transfer-test, participants worked on problems without provided representations to measure participant’s performance after they were exposed to external tools in the treatment-test. Results indicate that providing drawings or tables did not facilitate problem solving in general, which was against our hypothesis. If a representation was provided, a drawing was more helpful than a table, which was in line with our assumptions. However, the drawing effect was depending on the problem type and the level of pre-structuring. Obviously, simply providing external representations was not sufficient to facilitate problem solving. This speaks of the necessity of an early training in diagram literacy.

external representations, non-routine word problems, primary school, problem solving, drawings, tables